MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simpr1r Structured version   Visualization version   GIF version

Theorem simpr1r 1228
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
Assertion
Ref Expression
simpr1r ((𝜏 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜓)

Proof of Theorem simpr1r
StepHypRef Expression
1 simprr 771 . 2 ((𝜏 ∧ (𝜑𝜓)) → 𝜓)
213ad2antr1 1185 1 ((𝜏 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 394  w3a 1084
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 206  df-an 395  df-3an 1086
This theorem is referenced by:  poxp2  8148  oppccatid  17704  subccatid  17835  setccatid  18076  catccatid  18098  estrccatid  18125  xpccatid  18182  gsmsymgreqlem1  19397  dmdprdsplit  20016  neitr  23128  neitx  23555  tx1stc  23598  utop3cls  24200  metustsym  24508  clwwlkccat  29872  3pthdlem1  30046  archiabllem1  32993  esumpcvgval  33828  esum2d  33843  ifscgr  35771  btwnconn1lem8  35821  btwnconn1lem11  35824  btwnconn1lem12  35825  segletr  35841  broutsideof3  35853  unbdqndv2  36117  lhp2lt  39604  cdlemf2  40165  cdlemn11pre  40813  stoweidlem60  45586  isthincd2  48230  mndtccatid  48285
  Copyright terms: Public domain W3C validator
OSZAR »